{ "cells": [ { "cell_type": "markdown", "source": [ "# Lotka-Volterra Three Ways" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We will give three examples of deriving the Lotka-Volterra equations $$ \\dot r(t) = \\alpha r(t) - \\beta r(t)f(t), \\dot f(t) = \\gamma f(t) r(t) - \\delta f(t)$$ as a composition of primitive systems. First, we will show it as the composition of resource sharers where the undirected composition pattern is an undirected wiring diagram. Second, we will show it as the composition of machines where the directed composition pattern is a wiring diagram. Lastly, we will show it as the composition of machines where the directed composition pattern is an open circular port graph (open CPG)." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Although these examples are quite small and you can easily work them out by hand, this approach is based on the solid mathematical theory of operad algebras that allows you to scale to larger and more complex problems." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## Undirected composition\n", "### Undirected wiring diagrams" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "A standard Lotka-Volterra predator-prey model is the composition of three resource sharers:" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "1. a model of rabbit growth: this resource sharer has dynamics $\\dot r(t) = \\alpha r(t)$ and one port which exposes the rabbit population.\n", "2. a model of rabbit/fox predation: this resource sharer has dynamics $$\\dot r(t) = -\\beta r(t) f(t), \\dot f(t) = \\gamma r(t)f(t)$$ and two ports which expose the rabbit and fox populations respectively\n", "3. a model of fox population decline: this resource sharer has dynamics $\\dot f(t) = -\\delta f(t)$ and one port which exposes the fox population." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "However, there are not two independent rabbit populations --- one that grows and one that gets eaten by foxes. Likewise, there are not two independent fox populations --- one that declines and one that feasts on rabbits. To capture these interactions between the trio of resource sharers, we compose them by identifying the exposed rabbit populations and identifying the exposed fox populations." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: To maintain consistency with solution indexing, keyword argument vars will be removed in a future version. Please use keyword argument idxs instead.\n", "│ caller = ip:0x0\n", "└ @ Core :-1\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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p.α*u\n", "dotrf(u,p,t) = [-p.β*u[1]*u[2], p.γ*u[1]*u[2]]\n", "dotf(u,p,t) = -p.δ*u\n", "\n", "rabbit_growth = ContinuousResourceSharer{Float64}(1, dotr)\n", "rabbitfox_predation = ContinuousResourceSharer{Float64}(2, dotrf)\n", "fox_decline = ContinuousResourceSharer{Float64}(1, dotf)\n", "\n", "# Define the composition pattern\n", "rf = @relation (rabbits,foxes) begin\n", " growth(rabbits)\n", " predation(rabbits,foxes)\n", " decline(foxes)\n", "end\n", "\n", "# Compose\n", "rabbitfox_system = oapply(rf, [rabbit_growth, rabbitfox_predation, fox_decline])\n", "\n", "# Solve and plot\n", "u0 = [10.0, 100.0]\n", "params = LVector(α=.3, β=0.015, γ=0.015, δ=0.7)\n", "tspan = (0.0, 100.0)\n", "\n", "prob = ODEProblem(rabbitfox_system, u0, tspan, params)\n", "sol = solve(prob, Tsit5())\n", "\n", "plot(sol, rabbitfox_system,\n", " lw=2, title = \"Lotka-Volterra Predator-Prey Model\",\n", " xlabel = \"time\", ylabel = \"population size\"\n", ")" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "## Directed composition\n", "A standard Lotka-Volterra predator-prey model is the composition of two machines:" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "1. Evolution of a rabbit population: this machine has one input which represents a population of predators, $h(t)$, that hunt rabbits. This machine has one output which emits the rabbit population $r(t)$. The dynamics of this machine is the driven ODE $\\dot r(t) = \\alpha r(t) - \\beta r(t) h(t).$" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "2. Evoluation of a fox population: this machine has one input which represents a population of prey, $e(t)$, that are eaten by foxes. This machine has one output which emits the fox population $f(t)$. The dynamics of this machine is the driven ODE $\\dot f(t) =\\gamma f(t)e(t) - \\delta f(t).$" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "### Wiring diagrams\n", "Since foxes hunt rabbit, these machines compose by setting the fox population to be the input for rabbit evolution. Likewise, we set the rabbit population to be the input for fox evolution. We first implement this setting of inputs using a wiring diagram as our composition pattern." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: To maintain consistency with solution indexing, keyword argument vars will be removed in a future version. Please use keyword argument idxs instead.\n", "│ caller = ip:0x0\n", "└ @ Core :-1\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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ContinuousMachine{Float64}(1,1,1, dotf, (u, p, t) -> u)\n", "\n", "# Define the composition pattern\n", "rabbitfox_pattern = WiringDiagram([], [:rabbits, :foxes])\n", "rabbit_box = add_box!(rabbitfox_pattern, Box(:rabbit, [:pop], [:pop]))\n", "fox_box = add_box!(rabbitfox_pattern, Box(:fox, [:pop], [:pop]))\n", "\n", "add_wires!(rabbitfox_pattern, Pair[\n", " (rabbit_box, 1) => (fox_box, 1),\n", " (fox_box, 1) => (rabbit_box, 1),\n", " (rabbit_box, 1) => (output_id(rabbitfox_pattern), 1),\n", " (fox_box, 1) => (output_id(rabbitfox_pattern), 2)\n", "])\n", "\n", "# Compose\n", "rabbitfox_system = oapply(rabbitfox_pattern, [rabbit, fox])\n", "\n", "# Solve and plot\n", "u0 = [10.0, 100.0]\n", "params = LVector(α=.3, β=0.015, γ=0.015, δ=0.7)\n", "tspan = (0.0, 100.0)\n", "\n", "prob = ODEProblem(rabbitfox_system, u0, tspan, params)\n", "sol = solve(prob, Tsit5())\n", "\n", "plot(sol, rabbitfox_system, params,\n", " lw=2, title = \"Lotka-Volterra Predator-Prey Model\",\n", " xlabel = \"time\", ylabel = \"population size\"\n", ")" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "### Open CPG\n", "We next implement the setting of inputs using an open CPG as our composition pattern. We will use a barbell CPG. A barbell has two boxes connected by $n$ wires. In this instance we will set $n$ to $1$ since each machine receives and emits exactly one piece of information." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=2}", "image/png": 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"\n", "# Solve and plot\n", "u0 = [10.0, 100.0]\n", "params = LVector(α=.3, β=0.015, γ=0.015, δ=0.7)\n", "tspan = (0.0, 100.0)\n", "\n", "prob = ODEProblem(rabbitfox_system, u0, tspan, params)\n", "sol = solve(prob, FRK65(0))\n", "\n", "plot(sol, lw=2, bottom_margin=10mm, left_margin=10mm, title = \"Lotka-Volterra Predator-Prey Model\", label=[\"rabbits\" \"foxes\"])\n", "xlabel!(\"Time\")\n", "ylabel!(\"Population size\")" ], "metadata": {}, "execution_count": 3 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.3" }, "kernelspec": { "name": "julia-1.9", "display_name": "Julia 1.9.3", "language": "julia" } }, "nbformat": 4 }